This is non-cumulative. You need to be in a single game for 1 hour. I simply plugged my controller in, to keep it from turning off, loaded up the "Speed Run 4" game, went into the map and stood on a platform, and let my control sit while I got ready for work this morning. Shouldn't be hard to get at all.
Edit: Per Michael and some of the other comments below, you need to hit your sticks once or twice during that hour as the game will kick you for idling. Apologies for not mentioning that, as I believe I did hit them once or twice during the hour.
Edit: Others are reporting you can get this even with the disconnection, if you leave the game on. To be safe, I would definitely recommend moving the sticks once or twice to keep you from going idle.